Finite Group Databasebeta

← #20255725

Subgroups — #20255725

Order 6016.

398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689834C211yesmaximal, characteristic, complemented
2#15689793C211yesmaximal, characteristic
3#15689435C212yesmaximal, complemented
4#15689415C211yesmaximal, characteristic, complemented
5#15689368C212yesmaximal, complemented
6#15689320C211yesmaximal, characteristic, complemented
7#15689286C212yesmaximal, complemented
8C4×Dic188C211yesmaximal, characteristic, complemented
9#15689202C211yesmaximal, characteristic, complemented
10#15689121C212yesmaximal, complemented
11C47×#486C211yesmaximal, characteristic, complemented
12C2×#10625352C2212yes—
13C2×Dic188C2211yescharacteristic
14C2×#10625335C2212yes—
15C2×#10625324C2212yes—
16#13094020—21no—
17#13094015—21no—
18#13094004C2212yes—
19#13094000—22no—
20#13093996—22no—
21#13093995C2212yes—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24C4×D188C2211yescharacteristic
25D4×Dic47—21no—
26#13093986—21no—
27C4⋊C4×D47C2212yes—
28#13093958C2211yescharacteristic
29#13093957C2212yes—
30C4⋊(C47⋊C8)C2211yescharacteristic
31#13093949C2211yescharacteristic
32#13093949C2211yescharacteristic
33#13093947C2212yes—
34#13093945C2212yes—
35(C2×D47)⋊C8C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37#127×C47C2211yescharacteristic
38#102×C47C2212yes—
39#102×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2312yes—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C22×Dic47—22no—
48#10625352—24no—
49#10625352—42no—
50C2×D188D411yescharacteristic
51C2×C4×D47—22no—
52C2×C4×D47C2312yes—
53C2×Dic94C2311yescharacteristic
54C2×Dic94C2311yescharacteristic
55C2×C8×C47C2311yescharacteristic
56C2×C8×C47C2311yescharacteristic
57C4⋊C4×C47—21no—
58C4⋊C4×C47C2312yes—
59C42×C47C2311yescharacteristic
60C22⋊Dic47—22no—
61#10625335—42no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4D412yes—
64C4⋊Dic47—22no—
65C4⋊Dic47D411yescharacteristic
66C4⋊Dic47C2311yescharacteristic
67C4⋊Dic47C2311yescharacteristic
68Dic47⋊C4—21no—
69Dic47⋊C4—21no—
70Dic47⋊C4—22no—
71C4×Dic47—21no—
72C4×Dic47—21no—
73C2×C47⋊C8C2312yes—
74Dic188—22no—
75#10625324—42no—
76C23×C47—22no—
77C22×D47C2×D412yes—
78Q8×C47—81no—
79D4×C47—22no—
80D4×C47—22no—
81D4×C47—42no—
82D4×C47—81no—
83C2×C4×C47—22no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2411yescharacteristic
87C22⋊D47—44no—
88C22⋊D47—82no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—44no—
94C2×Dic47C2×D412yes—
95D188—22no—
96C4×D47—22no—
97C4×D47—22no—
98C4×D47—82no—
99Dic94—21no—
100Dic94—21no—
101Dic94—21no—
102Dic94#4112yes—
103C8×C47—21no—
104C8×C47—21no—
105C47⋊C8—22no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47C22×D411yescharacteristic
110C2×D47—22no—
111C2×D47—22no—
112C2×D47—22no—
113C4×C47—21no—
114C4×C47—42no—
115C4×C47#13712yes—
116C4×C47C2×#4111yescharacteristic
117C4×C47H(5,𝔽2)11yescharacteristic
118Dic47—22no—
119Dic47—22no—
120Dic47—41no—
121Dic47—41no—
122Dic47—41no—
123#3333—471nomaximal, Sylow
124C2×C47—82no—
125C2×C47#54611yescharacteristic
126C2×C47C2×#13711yescharacteristic
127C2×C47#57611yescharacteristic
128D47—42no—
129#554—471no—
130#550—471no—
131#486D4711yescharacteristic, complemented
132#480—472no—
133#477—471no—
134#468—472no—
135#460—471no—
136#452—472no—
137C4×Q16—471no—
138#436—471no—
139#417—472no—
140C47#333311yescharacteristic, complemented, Sylow
141C2×#41—472no—
142C2×Q16—471no—
143C2×SD16—472no—
144C2×M16—472no—
145C4⋊Q8C2×D4711yescharacteristic
146#127—941no—
147#127C2×D4711yescharacteristic
148#125—941no—
149C22⋊Q8—472no—
150C22⋊Q8—942no—
151#121—472no—
152#121—942no—
153C4×Q8—471no—
154C4×Q8—471no—
155C4×D4—471no—
156C4×D4—941no—
157C4×D4—941no—
158C2×C4⋊C4—472no—
159#107—471no—
160#107—472no—
161C4⋊C8—471no—
162#103—471no—
163#103—471no—
164#103—472no—
165#102—472no—
166#102C2×D4712yes—
167#102C2×D4712yes—
168C22⋊C8—472no—
169C4×C8C2×D4711yescharacteristic
170#41—944no—
171#41—1882no—
172C2×Q8—21no—
173C2×Q8—471no—
174C2×Q8—471no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—471no—
178C2×D4—942no—
179C2×D4—942no—
180C2×D4C22×D4712yes—
181C22×C4—472no—
182C22×C4—942no—
183C22×C4—942no—
184Q16—942no—
185SD16—1882no—
186M16—1882no—
187C2×C8—472no—
188C2×C8C22×D4711yescharacteristic
189C2×C8C22×D4711yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—471no—
192C4⋊C4—471no—
193C4⋊C4—471no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—941no—
197C4⋊C4—941no—
198C4⋊C4C22×D4712yes—
199C22⋊C4—472no—
200C22⋊C4—942no—
201C22⋊C4—942no—
202C42—941no—
203C42—941no—
204C42C22×D4711yescharacteristic
205C23—22no—
206C23—472no—
207Q8—81no—
208Q8—472no—
209Q8—941no—
210Q8—941no—
211Q8—941no—
212D4—22no—
213D4—22no—
214D4—42no—
215D4—81no—
216D4—942no—
217D4—3762no—
218D4—1884no—
219C2×C4—22no—
220C2×C4—472no—
221C2×C4—941no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—941no—
225C2×C4—941no—
226C2×C4—941no—
227C2×C4—3762no—
228C2×C4—1884no—
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4C23×D4711yescharacteristic
232C8—21no—
233C8—21no—
234C8—942no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—942no—
239C22—942no—
240C22—942no—
241C22C2×D4×D4711yescharacteristic
242C4—21no—
243C4—42no—
244C4—942no—
245C4—942no—
246C4—1881no—
247C4—1881no—
248C4—1881no—
249C4#1309405312yes—
250C4#41×D4711yescharacteristic
251C4#1309407011yescharacteristic
252C2—82no—
253C2—1882no—
254C2#1568976611yescharacteristic
255C2C2×#1309405311yescharacteristic
256C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3333
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689834C2semidirect
3. #15689435C2semidirect
4. #15689415C2semidirect
5. #15689368C2semidirect
6. #15689320C2semidirect
7. #15689286C2semidirect
8. C4×Dic188C2semidirect
9. #15689202C2semidirect
10. #15689121C2semidirect
11. C47×#486C2semidirect
131. #486D47semidirect
140. C47#3333semidirect